My mom was behind on mortgage, and has moved out of Florida to Marryland. We have caught up her mortgage and now reside in the home in Florida. The question is, can she quickclaim me the house and I be the only one on deed even though she currently has a mortgage? And I continue paying the note to her mortgage company. Thanks

No she can't "quick claim" you the property, but she may be able to QUIT claim you the property.

You need to discuss this with the mortgage lender. Most mortgages have a due on sale provision, so if the property changes hands, they can call the loan. A lender's security is a lien on the home and it can't change hands until the lien is satisfied unless they agree to it. They may agree to allowing mom to assign the mortgage to you. And then you can transfer ownership.